↑

Properties

Label 201.2.i.a
Level $201$
Weight $2$
Character orbit 201.i
Analytic conductor $1.605$
Analytic rank $0$
Dimension $50$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,2,Mod(22,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 201.i (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.60499308063\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(5\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 50 q - 2 q^{2} + 5 q^{3} - 6 q^{4} + 2 q^{5} - 9 q^{6} + 2 q^{7} + 27 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 50 q - 2 q^{2} + 5 q^{3} - 6 q^{4} + 2 q^{5} - 9 q^{6} + 2 q^{7} + 27 q^{8} - 5 q^{9} + 37 q^{10} - 15 q^{11} - 5 q^{12} - 4 q^{14} + 9 q^{15} - 17 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 2 q^{21} - q^{22} - 6 q^{23} + 6 q^{24} - 13 q^{25} + 22 q^{26} + 5 q^{27} - 39 q^{28} - 52 q^{29} + 18 q^{30} + 16 q^{31} - 35 q^{32} - 18 q^{33} - 14 q^{34} - 36 q^{35} + 5 q^{36} - 68 q^{37} + 20 q^{38} - 25 q^{40} + 30 q^{41} - 18 q^{42} + 33 q^{43} - 63 q^{44} + 2 q^{45} - 65 q^{46} - 38 q^{47} - 29 q^{49} + 21 q^{50} - 27 q^{51} - 38 q^{52} - 29 q^{53} + 2 q^{54} - q^{55} + 90 q^{56} + 24 q^{57} - 52 q^{58} + 35 q^{59} - 15 q^{60} + 30 q^{61} - 32 q^{62} - 20 q^{63} + 23 q^{64} + 6 q^{65} + 56 q^{66} + 10 q^{67} + 22 q^{68} + 6 q^{69} + 92 q^{70} + 2 q^{71} + 16 q^{72} - 40 q^{73} - 40 q^{74} + 13 q^{75} + 6 q^{76} + 86 q^{77} - 31 q^{79} + 26 q^{80} - 5 q^{81} + 90 q^{82} - 16 q^{83} + 72 q^{84} - 42 q^{85} + 92 q^{86} - 3 q^{87} - 48 q^{88} - 12 q^{89} + 37 q^{90} + 38 q^{91} - 60 q^{92} - 5 q^{93} - 62 q^{94} - 29 q^{95} + 24 q^{96} + 32 q^{97} + 9 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
22.1 −1.87424 + 0.550325i 0.142315 + 0.989821i 1.52739 − 0.981596i −1.74459 + 3.82012i −0.811455 − 1.77684i −0.0581100 + 0.0170626i 0.235861 − 0.272198i −0.959493 + 0.281733i 1.16746 − 8.11989i
22.2 −1.59954 + 0.469669i 0.142315 + 0.989821i 0.655446 − 0.421230i 1.13272 − 2.48031i −0.692527 − 1.51642i 0.0374006 − 0.0109818i 1.33282 − 1.53816i −0.959493 + 0.281733i −0.646912 + 4.49937i
22.3 −0.385020 + 0.113052i 0.142315 + 0.989821i −1.54705 + 0.994227i 0.0716395 − 0.156869i −0.166695 − 0.365012i −2.67716 + 0.786085i 1.00880 − 1.16422i −0.959493 + 0.281733i −0.00984831 + 0.0684965i
22.4 0.907634 − 0.266505i 0.142315 + 0.989821i −0.929732 + 0.597503i 1.48348 − 3.24837i 0.392963 + 0.860468i 4.49742 − 1.32056i −1.92355 + 2.21990i −0.959493 + 0.281733i 0.480750 − 3.34369i
22.5 2.15399 − 0.632468i 0.142315 + 0.989821i 2.55715 − 1.64338i −0.146077 + 0.319865i 0.932575 + 2.04206i −0.489834 + 0.143828i 1.52846 − 1.76393i −0.959493 + 0.281733i −0.112345 + 0.781375i
25.1 −0.381059 − 2.65032i 0.654861 − 0.755750i −4.96003 + 1.45640i −2.85080 + 1.83210i −2.25252 − 1.44761i −0.558441 − 3.88404i 3.52537 + 7.71949i −0.142315 − 0.989821i 5.94199 + 6.85742i
25.2 −0.254047 − 1.76694i 0.654861 − 0.755750i −1.13854 + 0.334305i 1.11491 − 0.716511i −1.50173 − 0.965101i 0.110811 + 0.770710i −0.603181 − 1.32078i −0.142315 − 0.989821i −1.54927 − 1.78795i
25.3 0.0345454 + 0.240269i 0.654861 − 0.755750i 1.86245 − 0.546865i 0.0517218 − 0.0332396i 0.204205 + 0.131235i −0.587961 − 4.08936i 0.397409 + 0.870204i −0.142315 − 0.989821i 0.00977317 + 0.0112788i
25.4 0.0704781 + 0.490186i 0.654861 − 0.755750i 1.68367 − 0.494370i −0.688821 + 0.442678i 0.416611 + 0.267740i 0.350196 + 2.43567i 0.772445 + 1.69142i −0.142315 − 0.989821i −0.265542 − 0.306451i
25.5 0.290637 + 2.02142i 0.654861 − 0.755750i −2.08270 + 0.611536i 2.61244 − 1.67891i 1.71802 + 1.10410i −0.145436 − 1.01153i −0.144754 − 0.316968i −0.142315 − 0.989821i 4.15306 + 4.79289i
40.1 −1.51073 − 1.74347i −0.415415 + 0.909632i −0.472767 + 3.28817i −2.59924 − 0.763205i 2.21349 − 0.649941i 0.716487 + 0.826871i 2.56560 − 1.64881i −0.654861 − 0.755750i 2.59611 + 5.68469i
40.2 −0.371960 − 0.429265i −0.415415 + 0.909632i 0.238716 − 1.66030i −2.09548 − 0.615288i 0.544991 − 0.160024i −1.13239 − 1.30685i −1.75717 + 1.12926i −0.654861 − 0.755750i 0.515313 + 1.12838i
40.3 0.260342 + 0.300451i −0.415415 + 0.909632i 0.262137 − 1.82320i 3.42699 + 1.00626i −0.381450 + 0.112004i −1.73782 − 2.00555i 1.28492 − 0.825765i −0.654861 − 0.755750i 0.589861 + 1.29161i
40.4 1.22439 + 1.41303i −0.415415 + 0.909632i −0.212872 + 1.48056i 1.12534 + 0.330431i −1.79397 + 0.526756i 1.59786 + 1.84403i 0.793078 − 0.509681i −0.654861 − 0.755750i 0.910957 + 1.99472i
40.5 1.65462 + 1.90953i −0.415415 + 0.909632i −0.623918 + 4.33945i −1.11429 − 0.327184i −2.42432 + 0.711846i −1.12665 − 1.30022i −5.06751 + 3.25669i −0.654861 − 0.755750i −1.21895 − 2.66913i
64.1 −1.87424 − 0.550325i 0.142315 − 0.989821i 1.52739 + 0.981596i −1.74459 − 3.82012i −0.811455 + 1.77684i −0.0581100 − 0.0170626i 0.235861 + 0.272198i −0.959493 − 0.281733i 1.16746 + 8.11989i
64.2 −1.59954 − 0.469669i 0.142315 − 0.989821i 0.655446 + 0.421230i 1.13272 + 2.48031i −0.692527 + 1.51642i 0.0374006 + 0.0109818i 1.33282 + 1.53816i −0.959493 − 0.281733i −0.646912 − 4.49937i
64.3 −0.385020 − 0.113052i 0.142315 − 0.989821i −1.54705 − 0.994227i 0.0716395 + 0.156869i −0.166695 + 0.365012i −2.67716 − 0.786085i 1.00880 + 1.16422i −0.959493 − 0.281733i −0.00984831 − 0.0684965i
64.4 0.907634 + 0.266505i 0.142315 − 0.989821i −0.929732 − 0.597503i 1.48348 + 3.24837i 0.392963 − 0.860468i 4.49742 + 1.32056i −1.92355 − 2.21990i −0.959493 − 0.281733i 0.480750 + 3.34369i
64.5 2.15399 + 0.632468i 0.142315 − 0.989821i 2.55715 + 1.64338i −0.146077 − 0.319865i 0.932575 − 2.04206i −0.489834 − 0.143828i 1.52846 + 1.76393i −0.959493 − 0.281733i −0.112345 − 0.781375i
See all 50 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 22.5
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
67.e even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 201.2.i.a ✓ 50
3.b odd 2 1 603.2.u.d 50
67.e even 11 1 inner 201.2.i.a ✓ 50
201.k odd 22 1 603.2.u.d 50
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
201.2.i.a ✓ 50 1.a even 1 1 trivial
201.2.i.a ✓ 50 67.e even 11 1 inner
603.2.u.d 50 3.b odd 2 1
603.2.u.d 50 201.k odd 22 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{50} + 2 T_{2}^{49} + 10 T_{2}^{48} + 11 T_{2}^{47} + 55 T_{2}^{46} + 127 T_{2}^{45} + 457 T_{2}^{44} + \cdots + 4489 \) acting on \(S_{2}^{\mathrm{new}}(201, [\chi])\). Copy content Toggle raw display